how is it possible to be a set of "Distinct" numbers and at the same time having two tens? what is the meaning of distinct here?

My versiion:

    s=[x%k for x in s]
    s1=[x for x in s if x!=0]
    if 0 in s:
        s1.append(0)
    counter=[0] * (k+1)
    for x in s1: 
        counter[x]+=1
    count=0;
    for i in range(0,k//2+1):
        max_k=max(counter)
        max_ind_rem=counter.index(max_k)
        if max_ind_rem*2==k:
            if max_ind_rem *2== k :
                count=count+1
            else:
                count=count+max(1, counter[k-max_ind_rem])
        else:
            count+=max_k
       #we include already
        counter[max_ind_rem]=0;
        counter[k-max_ind_rem]=0
    return count 

Fun puzzle! Here's a C# solution: ` static class NonDivisibleSubsetResult { private class MultiSetModK { private readonly Dictionary Counts; private readonly List distinct; private readonly Dictionary> PartnerDict;

    public MultiSetModK(List<int> source, int k)
    {
        List<int> modded = source.Select(x => x % k).ToList();
        Console.WriteLine("\tAfter modding: " + string.Join(',', modded));
        distinct = modded.Distinct().ToList();
        Counts = distinct.ToDictionary(
            a => a,
            a => modded.Count(b => b == a));

        PartnerDict =
        (from a in distinct
         let partners = new HashSet<int>(
             from b in distinct
             where (a + b) % k == 0
             select b)
         select new { a, partners })
        .ToDictionary(kvp => kvp.a, kvp => kvp.partners);
    }

    public int? MostPartneredElement()
    {
        var result = (from x in distinct
                      let partnerCount = (
                          from y in PartnerDict[x]
                          select y == x ? Counts[y] - 1 : Counts[y]) // Don't count an int as its own partner
                          .Sum()
                      where partnerCount > 0
                      select (x, partnerCount))
               .DefaultIfEmpty((-1, -1))
               .MaxBy(t => t.Item2);

        if (result.Item2 >= 0)
            Console.WriteLine($"{result.Item1} has {result.Item2} partners: {string.Join(',', PartnerDict[result.Item1])}");
        return result.Item2 < 0 ? (int?)null : result.Item1;
    }

    public void RemoveOneOf(int? x)
    {
        if (x == null) return;
        Console.WriteLine("Removing " + x.Value);

        Counts[x.Value] = Counts[x.Value] - 1;

        if (Counts[x.Value] == 0)
        {
            // If none left, purge from the other structures
            distinct.Remove(x.Value);

            foreach (var kvp in PartnerDict)
            {
                if (kvp.Value.Contains(x.Value))
                    kvp.Value.Remove(x.Value);
            }
        }

    }

    public int Count() => Counts.Values.Sum();

}

public static int nonDivisibleSubset(int k, List<int> s)
{
    MultiSetModK modded = new(s, k);

    // Iterate as long as there is an in in the modded list with partners
    for (int? x = modded.MostPartneredElement(); x != null; x = x = modded.MostPartneredElement())
    {
        modded.RemoveOneOf(x);
    }
    return modded.Count();

}

} `

I've been diving into the Non-Divisible Subset problem recently, and it's such a fascinating challenge! Finding that perfect subset with the right mod properties is like solving a fun puzzle. By the way, if you’re ever in Abu Dhabi and need some car TLC, check out Kia Service Abu Dhabi - Mussafah | Specialist Repair Workshop. They do top-notch work! Here’s the https://alzaabiautocare.com/brands/kia/ if you want to learn more about their services.